Question

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 34 feet up. the ladder makes an angle of 63° with the ground. find the length of the ladder. round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height (opposite side to the angle) is 34 feet, the angle with the ground is \(63^\circ\), and the ladder is the hypotenuse (\(h\)). We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(63^\circ)=\frac{34}{h}\).

Step2: Solve for \(h\)

Rearrange the formula to \(h = \frac{34}{\sin(63^\circ)}\). Calculate \(\sin(63^\circ)\approx0.8910\). Then \(h=\frac{34}{0.8910}\approx38.27\). Round to the nearest tenth: \(h\approx38.3\).

Answer:

The length of the ladder is approximately \(\boldsymbol{38.3}\) feet.